# Three-step alternating and preconditioned scheme for rectangular matrices

• Ashish Kumar Nandi
• Jajati Keshari Sahoo
• Pushpendu Ghosh
Original Research

## Abstract

In this article, a three-step alternating iterative scheme for rectangular system has been proposed. The convergence and comparison analysis of the proposed method has been discussed for the class of semi-monotone matrices and which confirms the faster convergence of our scheme. A preconditioned approach is also presented in this paper to relax the semi-monotonicity condition. The preconditioned approach is very promising and converges faster than some of existing schemes. We finally validated all the theoretical results by some numerical examples.

## Keywords

Nonnegativity Moore–Penrose inverse Semi-monotone Proper splitting Convergence theorem Comparison theorem

## Mathematics Subject Classification

15A09 65F10 65F15 65F20

## Notes

### Acknowledgements

We would like to thank Dr. Chinmay Kumar Giri, Lecturer, Department of Mathematics, Govt. Women’s College Baripada, India for his helpful suggestions. The authors also thank the referee for his/her helpful comments and suggestions which led to a much improved presentation of the paper.

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© Korean Society for Computational and Applied Mathematics 2018

## Authors and Affiliations

• Ashish Kumar Nandi
• 1
• Jajati Keshari Sahoo
• 1
• Pushpendu Ghosh
• 2
1. 1.Department of MathematicsBITS Pilani, K.K. Birla Goa CampusGoaIndia
2. 2.Department of Computer Science and Information SystemsBITS Pilani, K.K. Birla Goa CampusGoaIndia